Question

Question of AP ch.Try to solve it.

Answer 1

We can solve this problem in two way

1st

Given
Speed of thief =50m/min

In first two min only thief runs

Distance coverd by thief in first 2 min=100m

Now police speed in 1st min=60m/min

Increase 5m/min in every min

So now we policemen starts running after the thief distance between them=100m

The policemen and thief running in same direction then

Speed= speed of policemen - speed of thief

Extra distance to cover=100m

In 1st after police start running after the thief

Distance coverd by thief =50m

Distance coverd by policemen =60m

Extra distance covered by police
Distance between them =100-10=90m

Now in 2nd min

Thief will cover =50m,

Police will cover=60+5=65m

Extra distance =65-50=15

Distance between them =90-15=75m

In 3rd min

Thief=50m

Police =65+5=70

Extra=70-50=20

Distance between =75-20=55m

In 4th min

Thief =50m

Police =75m

Extra=75-50=25

Distance between =55-25=30m

In 5th min

Thief =50m

Police =80m

Extra =80-50=30

Distance between =30-30=0

So ans = In 5 min policemen will catch him.

If it is ask in question then

Write the total time after theft=5+2=7min



Now using Ap

Let police catch the thief after t minutes

Speed of thief =50m/min
distance covered by thief in (t+1)minutes =50m/min + (t+1)min=50(t+1)m

distance covered by police after t sec = sum of t terms in AP
where a = 50m/min is the first term and d = 5m/min is the common difference}

=T/2[2x50+(t-1)x5]

=t/2[100+5t-5]

=t/2[5t+95]

=2.5t²+47.5t

now, when police catches the thief ,

distance covered by thief = distance covered by police

2.5t²+47.5t=50(t+1)

2.5t²+47. 5t=50t+50

2.5t²-2.5t-50=0

(find two numbers who's sum =2.5 and multiple =2.5x25=125)

After solving root u will get these values of roots
t = 5,-4 but t≠ negative so, t = 5 min

The total time =7min


This is ur ans hope it will help you in case of any doubt comment below